The interplay of classes of algorithmically random objects

We study algorithmically random closed subsets of $2^\omega$, algorithmically random continuous functions from $2^\omega$ to $2^\omega$, and algorithmically random Borel probability measures on $2^\omega$, especially the interplay between these three classes of objects. Our main tools are preservation of randomness and its converse, the no randomness ex nihilo principle, which say together that given an almost-everywhere defined computable map between an effectively compact probability space and an effective Polish space, a real is Martin-L\"of random for the pushforward measure if and only if its preimage is random with respect to the measure on the domain. These tools allow us to prove new facts, some of which answer previously open questions, and reprove some known results more simply. Our main results are the following. First we answer an open question of Barmapalias, Brodhead, Cenzer, Remmel, and Weber by showing that $\mathcal{X}\subseteq2^\omega$ is a random closed set if and only if it is the set of zeros of a random continuous function on $2^\omega$. As a corollary we obtain the result that the collection of random continuous functions on $2^\omega$ is not closed under composition. Next, we construct a computable measure $Q$ on the space of measures on $2^\omega$ such that $\mathcal{X}\subseteq2^\omega$ is a random closed set if and only if $\mathcal{X}$ is the support of a $Q$-random measure. We also establish a correspondence between random closed sets and the random measures studied by Culver in previous work. Lastly, we study the ranges of random continuous functions, showing that the Lebesgue measure of the range of a random continuous function is always contained in $(0,1)$

High-density diffuse optical tomography for imaging human brain function

This review describes the unique opportunities and challenges for noninvasive optical mapping of human brain function. Diffuse optical methods offer safe, portable, and radiation free alternatives to traditional technologies like positron emission tomography or functional magnetic resonance imaging (fMRI). Recent developments in high-density diffuse optical tomography (HD-DOT) have demonstrated capabilities for mapping human cortical brain function over an extended field of view with image quality approaching that of fMRI. In this review, we cover fundamental principles of the diffusion of near infrared light in biological tissue. We discuss the challenges involved in the HD-DOT system design and implementation that must be overcome to acquire the signal-to-noise necessary to measure and locate brain function at the depth of the cortex. We discuss strategies for validation of the sensitivity, specificity, and reliability of HD-DOT acquired maps of cortical brain function. We then provide a brief overview of some clinical applications of HD-DOT. Though diffuse optical measurements of neurophysiology have existed for several decades, tremendous opportunity remains to advance optical imaging of brain function to address a crucial niche in basic and clinical neuroscience: that of bedside and minimally constrained high fidelity imaging of brain function

Conscious Identity Performance

Marginalized groups in the legal profession sometimes feel pressure to perform strategies to communicate their identity in a predominantly white legal profession. Relevant legal scholarship describes this phenomenon, for example, in terms such as covering and passing—largely forms of assimilation. The notion is that outsiders—women, people of color, LGBTQ—use these strategies to communicate with insiders—white, heterosexual, males—in ways designed to advance their status in the legal profession. This article expands on that scholarship by drawing on a theoretical framework that legal scholars have largely ignored: co-cultural theory. This interdisciplinary theory describes how non-dominant cultures communicate in a dominant society. In particular, the theory catalogs the micro-level communication practices outsiders employ to navigate their workplaces. This article is the first to apply co-cultural theory to legal scholarship. The overarching claim is that conscious identity performance is an indispensable step toward empowerment for outsiders in the legal profession, who might otherwise internalize the insiders’ stereotypes to their detriment

DESIGN, SYNTHESIS, AND PHARMACOLOGICAL EVALUATION OF THREE SERIES OF LOBELANE ANALOGS AS INHIBITORS OF THE VESICULAR MONOAMINE TRANSPORTER (VMAT2)

Methamphetamine (METH) abuse is a serious problem in the United States and worldwide. The reward experienced by METH users is due to the increase in extracellular dopamine (DA) concentrations caused by an interaction between METH and the DA transporter (DAT) as well as the Vesicular Monoamine Transporter-2 (VMAT2). The reward felt by users of METH leads to further use of the drug and subsequent abuse. The current project examined the ability of three novel series of lobelane analogs to interact with a binding site on the Vesicular Monoamine Transporter-2 (VMAT2) in an attempt to inhibit the effects of METH. Lobelane is a defunctionalized analog of Lobeline, a natural product found in Lobelia inflata which has been shown to bind to VMAT2 and inhibit its function. Rational drug design methodology and organic synthesis was used to generate a library of three series of lobelane analogs. In total, 107 compounds were synthesized and examined. Compounds were assayed for affinity in a high-throughput [3H] dihydrotetrabenazine (DTBZ) radioligand binding screen as well as for function in a [3H] DA uptake assay. Several compounds were identified which possess affinity as well as selectivity for the DTBZ binding site on VMAT2 [JPC-077 (Ki=0.19 μM), JPC-094 (Ki=0.15 μM), JPC-096 (Ki=0.19 μM), and JPC-106 (Ki=0.19 μM)]. The same four compounds exhibited inhibition of [3H]DA uptake [JPC-077 (Ki=9.3 nM), JPC-094 (Ki=13 nM), JPC-096 (Ki=20 nM), and JPC-106 (Ki=83 nM)]. With the assay data generated from the library of compounds, several structure activity relationship (SAR) based ligand based pharmacophore models were developed to guide future ligand design

On the K(1)-local homotopy of tmf boolean AND tmf

As a step towards understanding the $\mathrm{tmf}$-based Adams spectral sequence, we compute the $K(1)$-local homotopy of $\mathrm{tmf} \wedge \mathrm{tmf}$, using a small presentation of $L_{K(1)}\mathrm{tmf}$ due to Hopkins. We also describe the $K(1)$-local $\mathrm{tmf}$-based Adams spectral sequence

Evaluation of rigid registration methods for whole head imaging in diffuse optical tomography

Functional brain imaging has become an important neuroimaging technique for the study of brain organization and development. Compared to other imaging techniques, diffuse optical tomography (DOT) is a portable and low-cost technique that can be applied to infants and hospitalized patients using an atlas-based light model. For DOT imaging, the accuracy of the forward model has a direct effect on the resulting recovered brain function within a field of view and so the accuracy of the spatially normalized atlas-based forward models must be evaluated. Herein, the accuracy of atlas-based DOT is evaluated on models that are spatially normalized via a number of different rigid registration methods on 24 subjects. A multileveled approach is developed to evaluate the correlation of the geometrical and sensitivity accuracies across the full field of view as well as within specific functional subregions. Results demonstrate that different registration methods are optimal for recovery of different sets of functional brain regions. However, the “nearest point to point” registration method, based on the EEG 19 landmark system, is shown to be the most appropriate registration method for image quality throughout the field of view of the high-density cap that covers the whole of the optically accessible cortex

Brain Specificity of Diffuse Optical Imaging: Improvements from Superficial Signal Regression and Tomography

Functional near infrared spectroscopy (fNIRS) is a portable monitor of cerebral hemodynamics with wide clinical potential. However, in fNIRS, the vascular signal from the brain is often obscured by vascular signals present in the scalp and skull. In this paper, we evaluate two methods for improving in vivo data from adult human subjects through the use of high-density diffuse optical tomography (DOT). First, we test whether we can extend superficial regression methods (which utilize the multiple source–detector pair separations) from sparse optode arrays to application with DOT imaging arrays. In order to accomplish this goal, we modify the method to remove physiological artifacts from deeper sampling channels using an average of shallow measurements. Second, DOT provides three-dimensional image reconstructions and should explicitly separate different tissue layers. We test whether DOT's depth-sectioning can completely remove superficial physiological artifacts. Herein, we assess improvements in signal quality and reproducibility due to these methods using a well-characterized visual paradigm and our high-density DOT system. Both approaches remove noise from the data, resulting in cleaner imaging and more consistent hemodynamic responses. Additionally, the two methods act synergistically, with greater improvements when the approaches are used together